Plain R1soft-Idera backup does not directly support mySQL database backup.
But with this workaround you can backup your mySQL database too.
Run crontab in unix shell and create the rule to launch process for creating database backup:
0 0 * * * /usr/local/bin/mysqldump -uLOGIN -PPORT -hHOST -pPASS DBNAME | gzip -c > `date “+\%Y-\%m-\%d”`.gz
You can modify the script as needed to get a different schedule.
This script will create a .gz file with the backup of your database. It's an ordinary .gz file, and it will be normally backupped as any other files of your server.
Another way to do it is using MySQLDumper: a PHP and Perl based tool for backing up MySQL databases. You can easily dump your data into a backup file and - if needed - restore it. It is especially suited for shared hosting webspaces, where you don't have shell access. MySQLDumper is an open source project and released under the GNU-license.